Lyapunov Stability of Transformation Semigroups
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Beschreibung
This book presents recent research results on Lyapunov stability and attraction for semigroup actions in a pedagogical format, providing the reader with numerous modern ideas and mathematical formulations for dynamical concepts in the transformation group theory.
In recent decades, many fundamental concepts of dynamical systems have been extended to the general framework of transformation semigroups. Limit sets, attractors, isolated invariant sets, prolongational limit sets, and stable sets now have semigroup theoretical analogues. This monograph consolidates recent advancements in this field in a way that makes it accessible to graduate students. An effort was made to relate the presented results to important recurrence notions, for contextual clarity.
A rudimentary understanding of group theory and topology, including the concepts of semigroup action, orbit, fiber bundle, compactness, and connectedness, is a prerequisite for reading this text. As a valuable resource for research projects and academic dissertations on topological dynamics, geometry, and mathematical analysis, this work can potentially open new avenues for further research.
This book presents recent research results on Lyapunov stability and attraction for semigroup actions in a pedagogical format, providing the reader with numerous modern ideas and mathematical formulations for dynamical concepts in the transformation group theory.
In recent decades, many fundamental concepts of dynamical systems have been extended to the general framework of transformation semigroups. Limit sets, attractors, isolated invariant sets, prolongational limit sets, and stable sets now have semigroup theoretical analogues. This monograph consolidates recent advancements in this field in a way that makes it accessible to graduate students. An effort was made to relate the presented results to important recurrence notions, for contextual clarity.
A rudimentary understanding of group theory and topology, including the concepts of semigroup action, orbit, fiber bundle, compactness, and connectedness, is a prerequisite for reading this text. As a valuable resource for research projects and academic dissertations on topological dynamics, geometry, and mathematical analysis, this work can potentially open new avenues for further research.
Presents recent results on Lyapunov stability, currently available only in scattered literature Extends key concepts of dynamical systems to the general framework of transformation semigroups Makes advanced concepts accessible to graduate students for research and academic use
Autor*in
Victor H. L. Rocha
Themen in »Lyapunov Stability of Transformation Semigroups«
topological dynamics dynamical systems control theory smooth dynamical systems Lyapunov stability